The bicycle tire is generally provided with an air valve of the U.S. type or the French type. For this reason, two kinds of the bicycle air pumps must be used to inflate the bicycle tire. There are certain conventional bicycle air pumps which are provided with two connection heads engageable respectively with the air valve of the U.S. type and the air valve of the French type. For example, the U.S. patent Ser. No. 08/903,444 discloses an inflation device comprising two connection heads which are respectively adapted for the air valve of the U.S. type and the air valve of the French type. However, the inflation device in question is not user-friendly.